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K-State Today

March 12, 2015

Mathematics Colloquium Lecture March 12

Submitted by Reta McDermott

Gregory Arone, University of Virginia, will present "The Topological Tverberg Conjecture — A Survey" as part of the Mathematics Department Colloquium Lecture series at 2:30 p.m. Thursday, March 12, in 122 Cardwell Hall.

Tverberg's theorem is a classic result about convex hulls of sets of points in R^n. In 1981, Bárány, Shlosman, and Szűcs conjectured a topological generalization of the theorem, and proved it in a large class of cases. The general case of their conjecture has been an important problem in combinatorial topology ever since. Very recently, it was disproved by Florian Frick. I will explain the conjecture and some of the ideas that go into the proof of the theorem of Bárány, Shlosman, and Szűcs, and the counterexample of Frick. This will be a survey talk, and it should be accessible to graduate students.

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